Finite Group Databasebeta

← #32161128

Subgroups — #32161128

Order 18176.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986599C211yesmaximal, characteristic
2#22591489C211yesmaximal, characteristic, complemented
3#22591487C211yesmaximal, characteristic, complemented
4#22591484C211yesmaximal, characteristic, complemented
5#22591483C211yesmaximal, characteristic, complemented
6#22591433C211yesmaximal, characteristic, complemented
7#22591431C211yesmaximal, characteristic, complemented
8#22591403C211yesmaximal, characteristic, complemented
9#22591402C211yesmaximal, characteristic, complemented
10#22591331C211yesmaximal, characteristic, complemented
11#22591328C211yesmaximal, characteristic, complemented
12#22591326C211yesmaximal, characteristic, complemented
13#22591325C211yesmaximal, characteristic, complemented
14#22591286C211yesmaximal, characteristic, complemented
15#22591284C211yesmaximal, characteristic, complemented
16#22591247C211yesmaximal, characteristic, complemented
17#22591246C211yesmaximal, characteristic, complemented
18#22591042C211yesmaximal, characteristic, complemented
19#22591041C211yesmaximal, characteristic, complemented
20#22591037C211yesmaximal, characteristic, complemented
21#22591035C211yesmaximal, characteristic, complemented
22#22591030C211yesmaximal, characteristic, complemented
23#22591030C211yesmaximal, characteristic, complemented
24#22591030C211yesmaximal, characteristic, complemented
25#22591028C211yesmaximal, characteristic, complemented
26#22591027C211yesmaximal, characteristic, complemented
27#22590944C211yesmaximal, characteristic, complemented
28#22590850C211yesmaximal, characteristic, complemented
29C4×#14556100C211yesmaximal, characteristic, complemented
30#22590819C211yesmaximal, characteristic, complemented
31C71×#2325C211yesmaximal, characteristic, complemented
32#17986599C4116yescomplemented
33C2×#14556124C2211yescharacteristic
34C2×#14556118C2211yescharacteristic
35C2×#14556113C2211yescharacteristic
36C2×#14556111C2211yescharacteristic
37C2×#14556110C2211yescharacteristic
38C2×#14556109C2211yescharacteristic
39C2×#14556101C2211yescharacteristic
40C2×#14556100C2211yescharacteristic
41C2×#14556100C2211yescharacteristic
42C2×#14556100C2211yescharacteristic
43C2×#14556099C2211yescharacteristic
44C2×D4×Dic71C2211yescharacteristic
45C2×#14556090C2211yescharacteristic
46C2×C4×C22⋊D71C2211yescharacteristic
47C2×C4×C22⋊D71C2211yescharacteristic
48C2×C4×C22⋊D71C2211yescharacteristic
49C2×C4×C22⋊D71C2211yescharacteristic
50C2×C4×C22⋊D71C2211yescharacteristic
51C2×C4×C22⋊D71C2211yescharacteristic
52C2×(C22⋊D71)⋊C4C2211yescharacteristic
53C2×(C22⋊D71)⋊C4C2211yescharacteristic
54C2×(C22⋊D71)⋊C4C2211yescharacteristic
55C2×(C22⋊D71)⋊C4C2211yescharacteristic
56C2×#14556087C2211yescharacteristic
57C2×#14556086C2211yescharacteristic
58C2×#14556085C2211yescharacteristic
59C2×#14556084C2211yescharacteristic
60C2×#14556084C2211yescharacteristic
61C2×#14556084C2211yescharacteristic
62C22×C4×Dic71C2211yescharacteristic
63#17985902C2211yescharacteristic
64#17985902C2211yescharacteristic
65#17985902C2211yescharacteristic
66#17985901C2211yescharacteristic
67#17985899C2211yescharacteristic
68#17985899C2211yescharacteristic
69#17985899C2211yescharacteristic
70#17985899C2211yescharacteristic
71#17985899C2211yescharacteristic
72#17985899C2211yescharacteristic
73#17985899C2211yescharacteristic
74#17985899C2211yescharacteristic
75#17985898C2211yescharacteristic
76#17985896C2211yescharacteristic
77#17985896C2211yescharacteristic
78#17985896C2211yescharacteristic
79#17985896C2211yescharacteristic
80#17985896C2211yescharacteristic
81#17985896C2211yescharacteristic
82#17985896C2211yescharacteristic
83#17985895C2211yescharacteristic
84#17985894C2211yescharacteristic
85#17985894C2211yescharacteristic
86#17985894C2211yescharacteristic
87#17985893C2211yescharacteristic
88#17985893C2211yescharacteristic
89#17985893C2211yescharacteristic
90#17985893C2211yescharacteristic
91#17985892C2211yescharacteristic
92#17985892C2211yescharacteristic
93#17985891C2211yescharacteristic
94#17985891C2211yescharacteristic
95#17985889C2211yescharacteristic
96#17985889C2211yescharacteristic
97#17985888C2211yescharacteristic
98#17985888C2211yescharacteristic
99#17985888C2211yescharacteristic
100#17985888C2211yescharacteristic
101#17985887C2211yescharacteristic
102#17985887C2211yescharacteristic
103#17985887C2211yescharacteristic
104#17985887C2211yescharacteristic
105#17985886C2211yescharacteristic
106#17985886C2211yescharacteristic
107#17985884C2211yescharacteristic
108#17985883C2211yescharacteristic
109#17985882C2211yescharacteristic
110#17985881C2211yescharacteristic
111#17985881C2211yescharacteristic
112#17985881C2211yescharacteristic
113#17985880C2211yescharacteristic
114#17985880C2211yescharacteristic
115#17985879C2211yescharacteristic
116#17985879C2211yescharacteristic
117#17985878C2211yescharacteristic
118#17985878C2211yescharacteristic
119#17985878C2211yescharacteristic
120#17985877C2211yescharacteristic
121#17985877C2211yescharacteristic
122#17985876C2211yescharacteristic
123#17985875C2211yescharacteristic
124#17985875C2211yescharacteristic
125#17985875C2211yescharacteristic
126#17985875C2211yescharacteristic
127#17985874C2211yescharacteristic
128#17985874C2211yescharacteristic
129#17985873C2211yescharacteristic
130#17985873C2211yescharacteristic
131#17985873C2211yescharacteristic
132#17985873C2211yescharacteristic
133#17985873C2211yescharacteristic
134#17985872C2211yescharacteristic
135#17985872C2211yescharacteristic
136#17985872C2211yescharacteristic
137#17985872C2211yescharacteristic
138#17985872C2211yescharacteristic
139#17985871C2211yescharacteristic
140#17985870C2211yescharacteristic
141#17985868C2211yescharacteristic
142#17985863C2211yescharacteristic
143#17985859C2211yescharacteristic
144#17985858C2211yescharacteristic
145#17985858C2211yescharacteristic
146#17985857C2211yescharacteristic
147#17985857C2211yescharacteristic
148#17985857C2211yescharacteristic
149#17985857C2211yescharacteristic
150#17985856C2211yescharacteristic
151#17985856C2211yescharacteristic
152C4⋊C4×Dic71C2211yescharacteristic
153C4⋊C4×Dic71C2211yescharacteristic
154C4⋊C4×Dic71C2211yescharacteristic
155C4×Dic71⋊C4C2211yescharacteristic
156C4×Dic71⋊C4C2211yescharacteristic
157C4×Dic71⋊C4C2211yescharacteristic
158C4×C4⋊Dic71C2211yescharacteristic
159#17985850C2211yescharacteristic
160#17985850C2211yescharacteristic
161#17985850C2211yescharacteristic
162#17985850C2211yescharacteristic
163#17985850C2211yescharacteristic
164#17985850C2211yescharacteristic
165#17985850C2211yescharacteristic
166C22⋊C4×Dic71C2211yescharacteristic
167C4×(C2×D71)⋊C4C2211yescharacteristic
168C4×C22⋊Dic71C2211yescharacteristic
169#17985846C2211yescharacteristic
170C2×C71⋊#95C2211yescharacteristic
171#95×D71C2211yescharacteristic
172#95×D71C2211yescharacteristic
173C2×#121×C71C2211yescharacteristic
174C2×C4×D4×C71C2211yescharacteristic
175C2×C4×D4×C71C2211yescharacteristic
176#388×C71C2211yescharacteristic
177#388×C71C2211yescharacteristic
178#387×C71C2211yescharacteristic
179#387×C71C2211yescharacteristic
180#386×C71C2211yescharacteristic
181#386×C71C2211yescharacteristic
182#386×C71C2211yescharacteristic
183#386×C71C2211yescharacteristic
184#385×C71C2211yescharacteristic
185#385×C71C2211yescharacteristic
186#380×C71C2211yescharacteristic
187C2×#95×C71C2211yescharacteristic
188C22×D284C2311yescharacteristic
189C22×C22⋊D71C2311yescharacteristic
190C22×C22⋊D71C2311yescharacteristic
191C22×C22⋊D71C2311yescharacteristic
192C22×C22⋊D71C2311yescharacteristic
193C22×C22⋊D71C2311yescharacteristic
194C22×C22⋊D71C2311yescharacteristic
195C23×Dic71C2311yescharacteristic
196C23×Dic71C2311yescharacteristic
197C23×Dic71C2311yescharacteristic
198C23×Dic71C2311yescharacteristic
199C22×C4×D71C2311yescharacteristic
200C22×C4×D71C2311yescharacteristic
201C22×C4×D71C2311yescharacteristic
202C22×C4×D71C2311yescharacteristic
203C22×C4×D71C2311yescharacteristic
204C22×C4×D71C2311yescharacteristic
205#14556124C2×C418yescomplemented
206#14556118C2×C418yescomplemented
207#14556113C2×C418yescomplemented
208#14556111C2×C418yescomplemented
209#14556110C2×C418yescomplemented
210#14556109C2×C418yescomplemented
211#14556101C2×C418yescomplemented
212#14556100C2×C418yescomplemented
213#14556100C2×C418yescomplemented
214#14556100C2×C418yescomplemented
215#14556099C2×C418yescomplemented
216D4×Dic71—42no—
217#14556090—42no—
218C4×C22⋊D71—42no—
219C4×C22⋊D71—42no—
220C4×C22⋊D71—42no—
221C4×C22⋊D71—42no—
222C4×C22⋊D71—42no—
223C4×C22⋊D71C2×C418yescomplemented
224(C22⋊D71)⋊C4—42no—
225(C22⋊D71)⋊C4—42no—
226(C22⋊D71)⋊C4—42no—
227(C22⋊D71)⋊C4C2×C418yescomplemented
228#14556087—42no—
229#14556086—42no—
230#14556085—42no—
231#14556084—42no—
232#14556084—42no—
233#14556084C2×C418yescomplemented
234C2×C4⋊Dic71C2311yescharacteristic
235C2×C4⋊Dic71C2311yescharacteristic
236C2×C4⋊Dic71C2311yescharacteristic
237C2×C4⋊Dic71C2311yescharacteristic
238C2×C4⋊Dic71C2311yescharacteristic
239C2×C4⋊Dic71C2311yescharacteristic
240C2×C4⋊Dic71C2311yescharacteristic
241C2×Dic71⋊C4C2311yescharacteristic
242C2×Dic71⋊C4C2311yescharacteristic
243C2×Dic71⋊C4C2311yescharacteristic
244C2×Dic71⋊C4C2311yescharacteristic
245C2×Dic71⋊C4C2311yescharacteristic
246C2×Dic71⋊C4C2311yescharacteristic
247C2×Dic71⋊C4C2311yescharacteristic
248C2×Dic71⋊C4C2311yescharacteristic
249C2×Dic71⋊C4C2311yescharacteristic
250C2×Dic71⋊C4C2311yescharacteristic
251C2×Dic71⋊C4C2311yescharacteristic
252C2×Dic71⋊C4C2311yescharacteristic
253C2×Dic71⋊C4C2311yescharacteristic
254C2×Dic71⋊C4C2311yescharacteristic
255C2×Dic71⋊C4C2311yescharacteristic
256C2×Dic71⋊C4C2311yescharacteristic
257C2×Dic71⋊C4C2311yescharacteristic
258C2×Dic71⋊C4C2311yescharacteristic
259C2×Dic71⋊C4C2311yescharacteristic
260C2×Dic71⋊C4C2311yescharacteristic
261C2×Dic71⋊C4C2311yescharacteristic
262C2×Dic71⋊C4C2311yescharacteristic
263C2×C22⋊Dic71C2311yescharacteristic
264C2×C22⋊Dic71C2311yescharacteristic
265C2×C22⋊Dic71C2311yescharacteristic
266C2×C22⋊Dic71C2311yescharacteristic
267C2×C22⋊Dic71C2311yescharacteristic
268C2×C22⋊Dic71C2311yescharacteristic
269C2×C22⋊Dic71C2311yescharacteristic
270C2×C22⋊Dic71C2311yescharacteristic
271C2×C22⋊Dic71C2311yescharacteristic
272C2×C22⋊Dic71C2311yescharacteristic
273C2×C22⋊Dic71C2311yescharacteristic
274C2×C22⋊Dic71C2311yescharacteristic
275C2×C22⋊Dic71C2311yescharacteristic
276C2×C22⋊Dic71C2311yescharacteristic
277C2×(C2×D71)⋊C4C2311yescharacteristic
278C2×(C2×D71)⋊C4C2311yescharacteristic
279C2×(C2×D71)⋊C4C2311yescharacteristic
280C2×(C2×D71)⋊C4C2311yescharacteristic
281C2×(C2×D71)⋊C4C2311yescharacteristic
282C2×(C2×D71)⋊C4C2311yescharacteristic
283C2×(C2×D71)⋊C4C2311yescharacteristic
284C2×(C2×D71)⋊C4C2311yescharacteristic
285C2×(C2×D71)⋊C4C2311yescharacteristic
286C2×(C2×D71)⋊C4C2311yescharacteristic
287C2×(C2×D71)⋊C4C2311yescharacteristic
288C2×(C2×D71)⋊C4C2311yescharacteristic
289C2×(C2×D71)⋊C4C2311yescharacteristic
290C2×(C2×D71)⋊C4C2311yescharacteristic
291C2×(C2×D71)⋊C4C2311yescharacteristic
292C2×(C2×D71)⋊C4C2311yescharacteristic
293C2×C4×Dic71—42no—
294C2×C4×Dic71C2311yescharacteristic
295C2×C4×Dic71C2311yescharacteristic
296C2×C4×Dic71C2311yescharacteristic
297C2×C4×Dic71C2311yescharacteristic
298C2×C4×Dic71C2311yescharacteristic
299C2×C4×Dic71C2311yescharacteristic
300C2×C4×Dic71C2311yescharacteristic
301C2×C4×Dic71C2311yescharacteristic
302C2×C4×Dic71C2311yescharacteristic
303C2×C4×Dic71C2311yescharacteristic
304C2×C4×Dic71C2311yescharacteristic
305C2×C4×Dic71C2311yescharacteristic
306C2×C4×Dic71C2311yescharacteristic
307C2×C4×Dic71C2311yescharacteristic
308C2×C4×Dic71C2311yescharacteristic
309C2×C4×Dic71C2311yescharacteristic
310C2×C4×Dic71C2311yescharacteristic
311C2×C4×Dic71C2311yescharacteristic
312C71⋊#95C2311yescharacteristic
313C71⋊#95C2311yescharacteristic
314C71⋊#95C2311yescharacteristic
315C71⋊#95C2311yescharacteristic
316C71⋊#95C2311yescharacteristic
317C71⋊#95C2311yescharacteristic
318C71⋊#95C2311yescharacteristic
319C71⋊#95C2311yescharacteristic
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C71⋊#95C2311yescharacteristic
326C71⋊#95C2311yescharacteristic
327C71⋊#95C2311yescharacteristic
328C71⋊#95C2311yescharacteristic
329C71⋊#95C2311yescharacteristic
330C71⋊#95C2311yescharacteristic
331C71⋊#95C2311yescharacteristic
332C71⋊#95C2311yescharacteristic
333C71⋊#95C2311yescharacteristic
334C71⋊#95C2311yescharacteristic
335C71⋊#95C2311yescharacteristic
336C71⋊#95C2311yescharacteristic
337C71⋊#95C2311yescharacteristic
338C22×D4×C71C2311yescharacteristic
339C22×D4×C71C2311yescharacteristic
340C22×D4×C71C2311yescharacteristic
341C23×C4×C71C2311yescharacteristic
342C23×C4×C71C2311yescharacteristic
343C23×C4×C71C2311yescharacteristic
344C23×C4×C71C2311yescharacteristic
345C23×C4×C71C2311yescharacteristic
346#121×C71C2×C418yescomplemented
347C4×D4×C71—42no—
348C4×D4×C71—42no—
349C2×C4⋊C4×C71C2311yescharacteristic
350C2×C4⋊C4×C71C2311yescharacteristic
351C2×C4⋊C4×C71C2311yescharacteristic
352C2×C4⋊C4×C71C2311yescharacteristic
353C2×C4⋊C4×C71C2311yescharacteristic
354C2×C22⋊C4×C71C2311yescharacteristic
355C2×C22⋊C4×C71C2311yescharacteristic
356C2×C22⋊C4×C71C2311yescharacteristic
357C2×C22⋊C4×C71C2311yescharacteristic
358C2×C22⋊C4×C71C2311yescharacteristic
359C2×C22⋊C4×C71C2311yescharacteristic
360C2×C22⋊C4×C71C2311yescharacteristic
361C2×C22⋊C4×C71C2311yescharacteristic
362C2×C22⋊C4×C71C2311yescharacteristic
363C2×C22⋊C4×C71C2311yescharacteristic
364C2×C42×C71C2311yescharacteristic
365C2×C42×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369#95×C71C2311yescharacteristic
370#95×C71C2311yescharacteristic
371#95×C71C2311yescharacteristic
372#95×C71C2311yescharacteristic
373#95×C71C2311yescharacteristic
374#95×C71C2311yescharacteristic
375#95×C71C2311yescharacteristic
376C23×D71C2411yescharacteristic
377C23×D71C2411yescharacteristic
378C2×D284—41no—
379C2×D284—41no—
380C2×D284C22×C414yes—
381C2×C22⋊D71—22no—
382C2×C22⋊D71—22no—
383C2×C22⋊D71—22no—
384C2×C22⋊D71—22no—
385C2×C22⋊D71—41no—
386C2×C22⋊D71—41no—
387C2×C22⋊D71—41no—
388C2×C22⋊D71—41no—
389C2×C22⋊D71—41no—
390C2×C22⋊D71—41no—
391C2×C22⋊D71—41no—
392C2×C22⋊D71—41no—
393C2×C22⋊D71C22×C414yes—
394C2×C22⋊D71C22×C414yes—
395C2×C22⋊D71C22×C414yes—
396C2×C22⋊D71C22×C414yes—
397C2×C22⋊D71C22×C414yes—
398C2×C22⋊D71C22×C414yes—
399C22×Dic71—22no—
400C22×Dic71—22no—
401C22×Dic71—22no—
402C22×Dic71—22no—
403C22×Dic71—41no—
404C22×Dic71—41no—
405C22×Dic71—41no—
406C22×Dic71—41no—
407C22×Dic71—41no—
408C22×Dic71—41no—
409C22×Dic71C22×C414yes—
410C22×Dic71C22×C414yes—
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C22×Dic71C2411yescharacteristic
416C22×Dic71C2411yescharacteristic
417C22×Dic71C2411yescharacteristic
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C22×Dic71C2411yescharacteristic
423C22×Dic71C2411yescharacteristic
424C22×Dic71C2411yescharacteristic
425C2×C4×D71—22no—
426C2×C4×D71—22no—
427C2×C4×D71—41no—
428C2×C4×D71—41no—
429C2×C4×D71—41no—
430C2×C4×D71—41no—
431C2×C4×D71—41no—
432C2×C4×D71—41no—
433C2×C4×D71—41no—
434C2×C4×D71—41no—
435C2×C4×D71—41no—
436C2×C4×D71—41no—
437C2×C4×D71—41no—
438C2×C4×D71—41no—
439C2×C4×D71—41no—
440C2×C4×D71—41no—
441C2×C4×D71C22×C414yes—
442C2×C4×D71C22×C414yes—
443C4⋊Dic71—22no—
444C4⋊Dic71—41no—
445C4⋊Dic71—41no—
446C4⋊Dic71—41no—
447C4⋊Dic71—41no—
448C4⋊Dic71—41no—
449C4⋊Dic71C22×C414yes—
450Dic71⋊C4—22no—
451Dic71⋊C4—22no—
452Dic71⋊C4—22no—
453Dic71⋊C4—22no—
454Dic71⋊C4—22no—
455Dic71⋊C4—22no—
456Dic71⋊C4—41no—
457Dic71⋊C4—41no—
458Dic71⋊C4—41no—
459Dic71⋊C4—41no—
460Dic71⋊C4—41no—
461Dic71⋊C4—41no—
462Dic71⋊C4—41no—
463Dic71⋊C4—41no—
464Dic71⋊C4—41no—
465Dic71⋊C4—41no—
466Dic71⋊C4C22×C414yes—
467Dic71⋊C4C22×C414yes—
468Dic71⋊C4C22×C414yes—
469Dic71⋊C4C22×C414yes—
470Dic71⋊C4C22×C414yes—
471Dic71⋊C4C22×C414yes—
472C22⋊Dic71—22no—
473C22⋊Dic71—41no—
474C22⋊Dic71—41no—
475C22⋊Dic71—41no—
476C22⋊Dic71—41no—
477C22⋊Dic71—41no—
478C22⋊Dic71—41no—
479C22⋊Dic71—41no—
480C22⋊Dic71—41no—
481C22⋊Dic71—41no—
482C22⋊Dic71C22×C414yes—
483C22⋊Dic71C22×C414yes—
484C22⋊Dic71C22×C414yes—
485C22⋊Dic71C22×C414yes—
486(C2×D71)⋊C4—22no—
487(C2×D71)⋊C4—22no—
488(C2×D71)⋊C4—41no—
489(C2×D71)⋊C4—41no—
490(C2×D71)⋊C4—41no—
491(C2×D71)⋊C4—41no—
492(C2×D71)⋊C4—41no—
493(C2×D71)⋊C4—41no—
494(C2×D71)⋊C4—41no—
495(C2×D71)⋊C4—41no—
496(C2×D71)⋊C4—41no—
497(C2×D71)⋊C4—41no—
498(C2×D71)⋊C4C22×C414yes—
499(C2×D71)⋊C4C22×C414yes—
500(C2×D71)⋊C4C22×C414yes—
501(C2×D71)⋊C4C22×C414yes—
502C4×Dic71—22no—
503C4×Dic71—22no—
504C4×Dic71—22no—
505C4×Dic71—22no—
506C4×Dic71—22no—
507C4×Dic71—22no—
508C4×Dic71—22no—
509C4×Dic71—41no—
510C4×Dic71—41no—
511C4×Dic71—41no—
512C4×Dic71—41no—
513C4×Dic71—41no—
514C4×Dic71—41no—
515C4×Dic71—41no—
516C4×Dic71—41no—
517C4×Dic71—41no—
518C4×Dic71C22×C414yes—
519C4×Dic71C22×C414yes—
520C24×C71C2411yescharacteristic
521C24×C71C2411yescharacteristic
522C24×C71C2411yescharacteristic
523C2×D4×C71—41no—
524C2×D4×C71—41no—
525C2×D4×C71—41no—
526C2×D4×C71—41no—
527C2×D4×C71—41no—
528C2×D4×C71—41no—
529C2×D4×C71C22×C414yes—
530C2×D4×C71C22×C414yes—
531C2×D4×C71C22×C414yes—
532C22×C4×C71—22no—
533C22×C4×C71—22no—
534C22×C4×C71—41no—
535C22×C4×C71—41no—
536C22×C4×C71—41no—
537C22×C4×C71—41no—
538C22×C4×C71—41no—
539C22×C4×C71—41no—
540C22×C4×C71—41no—
541C22×C4×C71—41no—
542C22×C4×C71—41no—
543C22×C4×C71—41no—
544C22×C4×C71—41no—
545C22×C4×C71—41no—
546C22×C4×C71C22×C414yes—
547C22×C4×C71C2411yescharacteristic
548C22×C4×C71C2411yescharacteristic
549C22×C4×C71C2411yescharacteristic
550C22×C4×C71C2411yescharacteristic
551C22×C4×C71C2411yescharacteristic
552C22×C4×C71C2411yescharacteristic
553C22×C4×C71C2411yescharacteristic
554C22×C4×C71C2411yescharacteristic
555C22×C4×C71C2411yescharacteristic
556C22×C4×C71C2411yescharacteristic
557C22×C4×C71C2411yescharacteristic
558C22×C4×C71C2411yescharacteristic
559C4⋊C4×C71—22no—
560C4⋊C4×C71—41no—
561C4⋊C4×C71—41no—
562C4⋊C4×C71—41no—
563C4⋊C4×C71C22×C414yes—
564C22⋊C4×C71—22no—
565C22⋊C4×C71—41no—
566C22⋊C4×C71—41no—
567C22⋊C4×C71—41no—
568C22⋊C4×C71—41no—
569C22⋊C4×C71—41no—
570C22⋊C4×C71—41no—
571C22⋊C4×C71—41no—
572C22⋊C4×C71C22×C414yes—
573C22⋊C4×C71C22×C414yes—
574C42×C71—22no—
575C42×C71—41no—
576C23×C71—21no—
577C23×C71—21no—
578C23×C71—21no—
579C23×C71—21no—
580C23×C71—21no—
581C23×C71—21no—
582C23×C71—21no—
583C23×C71—21no—
584C23×C71—21no—
585C23×C71—21no—
586C23×C71—21no—
587C23×C71—21no—
588C23×C71—21no—
589C23×C71—21no—
590C23×C71—21no—
591C23×C71—21no—
592C23×C71—21no—
593C23×C71—21no—
594C23×C71C23×C412yes—
595C23×C71C23×C412yes—
596C23×C71C23×C412yes—
597C23×C71C2511yescharacteristic
598C22×D71—21no—
599C22×D71—21no—
600C22×D71—21no—
601C22×D71—21no—
602C22×D71—21no—
603C22×D71—21no—
604C22×D71—21no—
605C22×D71—21no—
606C22×D71—21no—
607C22×D71—21no—
608C22×D71—21no—
609C22×D71—21no—
610C22×D71C23×C412yes—
611C22×D71C23×C412yes—
612D4×C71—44no—
613D4×C71—44no—
614D4×C71—44no—
615C2×C4×C71—21no—
616C2×C4×C71—21no—
617C2×C4×C71—21no—
618C2×C4×C71—21no—
619C2×C4×C71—21no—
620C2×C4×C71—21no—
621C2×C4×C71—21no—
622C2×C4×C71—21no—
623C2×C4×C71—21no—
624C2×C4×C71—21no—
625C2×C4×C71—21no—
626C2×C4×C71—21no—
627C2×C4×C71—21no—
628C2×C4×C71—21no—
629C2×C4×C71—21no—
630C2×C4×C71—21no—
631C2×C4×C71—21no—
632C2×C4×C71—21no—
633C2×C4×C71—21no—
634C2×C4×C71—21no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—21no—
644C2×C4×C71—21no—
645C2×C4×C71—21no—
646C2×C4×C71—44no—
647C2×C4×C71—44no—
648C2×C4×C71—82no—
649C2×C4×C71—82no—
650C2×C4×C71—82no—
651C2×C4×C71C23×C412yes—
652C2×C4×C71C23×C412yes—
653C2×C4×C71C23×C412yes—
654C2×C4×C71C23×C412yes—
655C2×C4×C71H(5,𝔽2)12yes—
656C22⋊D71—28no—
657C22⋊D71—28no—
658C22⋊D71—44no—
659C22⋊D71—44no—
660C22⋊D71—44no—
661C22⋊D71—44no—
662C2×Dic71—21no—
663C2×Dic71—21no—
664C2×Dic71—21no—
665C2×Dic71—21no—
666C2×Dic71—21no—
667C2×Dic71—21no—
668C2×Dic71—21no—
669C2×Dic71—21no—
670C2×Dic71—21no—
671C2×Dic71—21no—
672C2×Dic71—21no—
673C2×Dic71—21no—
674C2×Dic71—28no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—21no—
683C2×Dic71—21no—
684C2×Dic71—21no—
685C2×Dic71—21no—
686C2×Dic71—21no—
687C2×Dic71—21no—
688C2×Dic71—21no—
689C2×Dic71—21no—
690C2×Dic71—21no—
691C2×Dic71—21no—
692C2×Dic71—21no—
693C2×Dic71—21no—
694C2×Dic71—21no—
695C2×Dic71—21no—
696C2×Dic71—44no—
697C2×Dic71—44no—
698C2×Dic71—82no—
699C2×Dic71C23×C412yes—
700C2×Dic71C23×C412yes—
701C2×Dic71C23×C412yes—
702C2×Dic71C23×C412yes—
703C2×Dic71C23×C412yes—
704C2×Dic71C23×C412yes—
705C2×Dic71H(5,𝔽2)12yes—
706C2×Dic71H(5,𝔽2)12yes—
707C2×Dic712−1+412yes—
708D284—44no—
709C4×D71—44no—
710C4×D71—44no—
711C4×D71—82no—
712C4×D71—82no—
713C4×D71—82no—
714C4×D71—82no—
715C22×C71—22no—
716C22×C71—22no—
717C22×C71—22no—
718C22×C71—22no—
719C22×C71—22no—
720C22×C71—22no—
721C22×C71—22no—
722C22×C71—22no—
723C22×C71—22no—
724C22×C71—41no—
725C22×C71—41no—
726C22×C71—41no—
727C22×C71—41no—
728C22×C71—41no—
729C22×C71—41no—
730C22×C71—41no—
731C22×C71—41no—
732C22×C71—41no—
733C22×C71—41no—
734C22×C71—41no—
735C22×C71—41no—
736C22×C71C24×C411yescharacteristic
737C22×C71C2×H(5,𝔽2)11yescharacteristic
738C22×C71C2×H(5,𝔽2)11yescharacteristic
739C22×C71C2×H(5,𝔽2)11yescharacteristic
740C22×C71C2×2−1+411yescharacteristic
741C22×C71#58511yescharacteristic
742C22×C71#58511yescharacteristic
743C2×D71—22no—
744C2×D71—22no—
745C2×D71—22no—
746C2×D71—22no—
747C2×D71—22no—
748C2×D71—22no—
749C2×D71—41no—
750C2×D71—41no—
751C2×D71—41no—
752C2×D71—41no—
753C2×D71—41no—
754C2×D71—41no—
755C2×D71—41no—
756C2×D71—41no—
757C4×C71—22no—
758C4×C71—22no—
759C4×C71—22no—
760C4×C71—22no—
761C4×C71—22no—
762C4×C71—41no—
763C4×C71—41no—
764C4×C71—41no—
765C4×C71—41no—
766C4×C71—41no—
767C4×C71—41no—
768C4×C71—41no—
769Dic71—22no—
770Dic71—22no—
771Dic71—22no—
772Dic71—22no—
773Dic71—22no—
774Dic71—22no—
775Dic71—41no—
776Dic71—41no—
777Dic71—41no—
778Dic71—41no—
779Dic71—41no—
780Dic71—41no—
781Dic71—41no—
782Dic71#52014yes—
783#34423—711nomaximal, Sylow
784C2×C71—42no—
785C2×C71—42no—
786C2×C71—42no—
787C2×C71C2×#52011yescharacteristic
788C2×C71C4×H(5,𝔽2)11yescharacteristic
789C2×C71C4×H(5,𝔽2)11yescharacteristic
790C2×C71#354211yescharacteristic
791C2×C71#354211yescharacteristic
792C2×C71#354811yescharacteristic
793C2×C71#355711yescharacteristic
794D71—42no—
795D71—42no—
796C2×#540—711no—
797#2376—711no—
798#2376—711no—
799#2376—711no—
800#2376—711no—
801#2370—711no—
802#2370—711no—
803#2366—711no—
804#2366—711no—
805#2359—711no—
806#2359—711no—
807#2359—711no—
808#2359—711no—
809#2354—711no—
810#2354—711no—
811#2349—711no—
812#2349—711no—
813#2325—711no—
814#2325—711no—
815#2325—711no—
816#2325D7111yescharacteristic, complemented
817#2324—711no—
818#2324—711no—
819#2324—711no—
820#2324—711no—
821#2324—711no—
822#2324—711no—
823#2314—711no—
824C4×#121—711no—
825C4×#121—711no—
826#2296—711no—
827C71#3442311yescharacteristic, complemented, Sylow
828#540—7116no—
829C2×#127—711no—
830C2×#125—711no—
831C2×#123—711no—
832C2×#123—711no—
833C2×#123—711no—
834C2×#123—711no—
835C2×#121—711no—
836C2×#121—711no—
837C2×#121—711no—
838C2×#121—711no—
839C2×#121—711no—
840C2×#121C2×D7111yescharacteristic
841C2×C4×D4—711no—
842C2×C4×D4—711no—
843C2×C4×D4—711no—
844C2×C4×D4—711no—
845C2×C4×D4—711no—
846C2×C4×D4—711no—
847C2×C4×D4—711no—
848C2×C4×D4—711no—
849C2×C4×D4—711no—
850C2×C4×D4—711no—
851C2×C4×D4—711no—
852C2×C4×D4—711no—
853C2×C4×D4C2×D7111yescharacteristic
854C2×C4×D4C2×D7111yescharacteristic
855C2×#117—711no—
856C2×#117—711no—
857C2×#117—711no—
858C2×#117—711no—
859C2×#117—711no—
860C2×#117—711no—
861C22×C42—711no—
862#390—711no—
863#390—711no—
864#390—711no—
865#390—711no—
866#390—711no—
867#390—711no—
868#390—711no—
869#390—711no—
870#390—711no—
871#390—711no—
872#390—711no—
873#390—711no—
874#389—711no—
875#389—711no—
876#389—711no—
877#389—711no—
878#389—711no—
879#389—711no—
880#389—711no—
881#389—711no—
882#389—711no—
883#389—711no—
884#389—711no—
885#389—711no—
886#388—711no—
887#388—711no—
888#388—711no—
889#388—711no—
890#388—711no—
891#388—711no—
892#388—711no—
893#388—711no—
894#388—711no—
895#388—711no—
896#388—711no—
897#388—711no—
898#388—711no—
899#388—711no—
900#388—711no—
901#388—711no—
902#388—711no—
903#388—711no—
904#388C2×D7111yescharacteristic
905#388C2×D7111yescharacteristic
906#387—711no—
907#387—711no—
908#387—711no—
909#387—711no—
910#387—711no—
911#387—711no—
912#387—711no—
913#387—711no—
914#387—711no—
915#387—711no—
916#387C2×D7111yescharacteristic
917#387C2×D7111yescharacteristic
918#386—711no—
919#386—711no—
920#386—711no—
921#386—711no—
922#386—711no—
923#386—711no—
924#386—711no—
925#386—711no—
926#386—711no—
927#386—711no—
928#386—711no—
929#386—711no—
930#386C2×D7111yescharacteristic
931#386C2×D7111yescharacteristic
932#386C2×D7111yescharacteristic
933#386C2×D7111yescharacteristic
934#385—711no—
935#385—711no—
936#385—711no—
937#385—711no—
938#385—711no—
939#385—711no—
940#385—711no—
941#385—711no—
942#385—711no—
943#385—711no—
944#385—711no—
945#385—711no—
946#385—711no—
947#385—711no—
948#385C2×D7111yescharacteristic
949#385C2×D7111yescharacteristic
950#384—711no—
951#382—711no—
952#380—711no—
953#380—711no—
954#380—711no—
955#380—711no—
956#380—711no—
957#380—711no—
958#380—711no—
959#380—711no—
960#380—711no—
961#380C2×D7111yescharacteristic
962C4×C4⋊C4—711no—
963C4×C4⋊C4—711no—
964C4×C4⋊C4—711no—
965C4×C4⋊C4—711no—
966C4×C4⋊C4—711no—
967C4×C4⋊C4—711no—
968C4×C4⋊C4—711no—
969C4×C4⋊C4—711no—
970C4×C4⋊C4—711no—
971C4×C4⋊C4—711no—
972C4×C4⋊C4—711no—
973C4×C4⋊C4—711no—
974C4×C4⋊C4—711no—
975C4×C4⋊C4—711no—
976C4×C22⋊C4—711no—
977C4×C22⋊C4—711no—
978C4×C22⋊C4—711no—
979C4×C22⋊C4—711no—
980C2×#95—711no—
981C2×#95—711no—
982C2×#95—711no—
983C2×#95C2×D7111yescharacteristic
984C22×D4—711no—
985C22×D4—711no—
986C22×D4—711no—
987C22×D4—711no—
988C22×D4—711no—
989C22×D4—711no—
990C22×D4—711no—
991C22×D4C22×D7111yescharacteristic
992C22×D4C22×D7111yescharacteristic
993C22×D4C22×D7111yescharacteristic
994C23×C4—711no—
995C23×C4—711no—
996C23×C4—711no—
997C23×C4—711no—
998C23×C4—711no—
999C23×C4—711no—
1000C23×C4—711no—
1001C23×C4—711no—
1002C23×C4—711no—
1003C23×C4—711no—
1004C23×C4C22×D7111yescharacteristic
1005C23×C4C22×D7111yescharacteristic
1006C23×C4C22×D7111yescharacteristic
1007C23×C4C22×D7111yescharacteristic
1008C23×C4C22×D7111yescharacteristic
1009#127—718no—
1010#125—718no—
1011#123—718no—
1012#123—718no—
1013#123—718no—
1014#123—718no—
1015#121—718no—
1016#121—718no—
1017#121—718no—
1018#121—718no—
1019#121—718no—
1020#121C4×D7118yescomplemented
1021C4×D4—42no—
1022C4×D4—42no—
1023C4×D4—2842no—
1024C4×D4—2842no—
1025C4×D4—2842no—
1026C4×D4—2842no—
1027C4×D4—2842no—
1028C4×D4—2842no—
1029C4×D4—2842no—
1030C4×D4—2842no—
1031C4×D4—2842no—
1032C4×D4—2842no—
1033C4×D4—718no—
1034C4×D4—718no—
1035#117—2842no—
1036#117—2842no—
1037#117—2842no—
1038#117—2842no—
1039#117—2842no—
1040#117—718no—
1041C2×C4⋊C4—711no—
1042C2×C4⋊C4—711no—
1043C2×C4⋊C4—711no—
1044C2×C4⋊C4—711no—
1045C2×C4⋊C4—711no—
1046C2×C4⋊C4—711no—
1047C2×C4⋊C4—711no—
1048C2×C4⋊C4—711no—
1049C2×C4⋊C4—711no—
1050C2×C4⋊C4—711no—
1051C2×C4⋊C4—711no—
1052C2×C4⋊C4—711no—
1053C2×C4⋊C4—711no—
1054C2×C4⋊C4—711no—
1055C2×C4⋊C4—711no—
1056C2×C4⋊C4—711no—
1057C2×C4⋊C4—711no—
1058C2×C4⋊C4—711no—
1059C2×C4⋊C4—711no—
1060C2×C4⋊C4—711no—
1061C2×C4⋊C4—711no—
1062C2×C4⋊C4—711no—
1063C2×C4⋊C4—711no—
1064C2×C4⋊C4—711no—
1065C2×C4⋊C4—711no—
1066C2×C4⋊C4—711no—
1067C2×C4⋊C4—711no—
1068C2×C4⋊C4—711no—
1069C2×C4⋊C4—711no—
1070C2×C4⋊C4C22×D7111yescharacteristic
1071C2×C4⋊C4C22×D7111yescharacteristic
1072C2×C4⋊C4C22×D7111yescharacteristic
1073C2×C4⋊C4C22×D7111yescharacteristic
1074C2×C4⋊C4C22×D7111yescharacteristic
1075C2×C22⋊C4—711no—
1076C2×C22⋊C4—711no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—711no—
1082C2×C22⋊C4—711no—
1083C2×C22⋊C4—711no—
1084C2×C22⋊C4—711no—
1085C2×C22⋊C4—711no—
1086C2×C22⋊C4—711no—
1087C2×C22⋊C4—711no—
1088C2×C22⋊C4—711no—
1089C2×C22⋊C4—711no—
1090C2×C22⋊C4—711no—
1091C2×C22⋊C4—711no—
1092C2×C22⋊C4—711no—
1093C2×C22⋊C4—711no—
1094C2×C22⋊C4—711no—
1095C2×C22⋊C4—711no—
1096C2×C22⋊C4—711no—
1097C2×C22⋊C4—711no—
1098C2×C22⋊C4—711no—
1099C2×C22⋊C4—711no—
1100C2×C22⋊C4—711no—
1101C2×C22⋊C4—711no—
1102C2×C22⋊C4—711no—
1103C2×C22⋊C4—711no—
1104C2×C22⋊C4—711no—
1105C2×C22⋊C4C22×D7111yescharacteristic
1106C2×C22⋊C4C22×D7111yescharacteristic
1107C2×C22⋊C4C22×D7111yescharacteristic
1108C2×C22⋊C4C22×D7111yescharacteristic
1109C2×C22⋊C4C22×D7111yescharacteristic
1110C2×C22⋊C4C22×D7111yescharacteristic
1111C2×C22⋊C4C22×D7111yescharacteristic
1112C2×C22⋊C4C22×D7111yescharacteristic
1113C2×C22⋊C4C22×D7111yescharacteristic
1114C2×C22⋊C4C22×D7111yescharacteristic
1115C2×C42—2842no—
1116C2×C42—711no—
1117C2×C42—711no—
1118C2×C42—711no—
1119C2×C42—711no—
1120C2×C42—711no—
1121C2×C42—711no—
1122C2×C42—711no—
1123C2×C42—711no—
1124C2×C42—711no—
1125C2×C42—711no—
1126C2×C42—711no—
1127C2×C42—711no—
1128C2×C42—711no—
1129C2×C42—711no—
1130C2×C42—711no—
1131C2×C42—711no—
1132C2×C42—711no—
1133C2×C42—711no—
1134C2×C42C22×D7111yescharacteristic
1135C2×C42C22×D7111yescharacteristic
1136#95—711no—
1137#95—711no—
1138#95—711no—
1139#95—711no—
1140#95—711no—
1141#95—711no—
1142#95—711no—
1143#95—711no—
1144#95—711no—
1145#95—711no—
1146#95—711no—
1147#95—711no—
1148#95—711no—
1149#95—711no—
1150#95—711no—
1151#95—711no—
1152#95—711no—
1153#95—711no—
1154#95—711no—
1155#95—711no—
1156#95—711no—
1157#95—711no—
1158#95—711no—
1159#95—711no—
1160#95—711no—
1161#95—711no—
1162#95C22×D7111yescharacteristic
1163#95C22×D7111yescharacteristic
1164#95C22×D7111yescharacteristic
1165#95C22×D7111yescharacteristic
1166#95C22×D7111yescharacteristic
1167#95C22×D7111yescharacteristic
1168#95C22×D7111yescharacteristic
1169#95C22×D7111yescharacteristic
1170#95C22×D7111yescharacteristic
1171#95C22×D7111yescharacteristic
1172C24—711no—
1173C24—711no—
1174C24C23×D7111yescharacteristic
1175C24C23×D7111yescharacteristic
1176C24C23×D7111yescharacteristic
1177C2×D4—41no—
1178C2×D4—41no—
1179C2×D4—41no—
1180C2×D4—41no—
1181C2×D4—41no—
1182C2×D4—41no—
1183C2×D4—2841no—
1184C2×D4—2841no—
1185C2×D4—2841no—
1186C2×D4—2841no—
1187C2×D4—2841no—
1188C2×D4—2841no—
1189C2×D4—2841no—
1190C2×D4—2841no—
1191C2×D4—2841no—
1192C2×D4—2841no—
1193C2×D4—714no—
1194C2×D4—714no—
1195C2×D4—714no—
1196C2×D4—714no—
1197C2×D4—714no—
1198C2×D4—714no—
1199C2×D4—714no—
1200C2×D4—1422no—
1201C2×D4—1422no—
1202C2×D4—1422no—
1203C2×D4—1422no—
1204C2×D4C2×C4×D7114yes—
1205C2×D4C2×C4×D7114yes—
1206C2×D4C2×C4×D7114yes—
1207C22×C4—22no—
1208C22×C4—22no—
1209C22×C4—41no—
1210C22×C4—41no—
1211C22×C4—41no—
1212C22×C4—41no—
1213C22×C4—41no—
1214C22×C4—41no—
1215C22×C4—41no—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—2841no—
1222C22×C4—2841no—
1223C22×C4—2841no—
1224C22×C4—2841no—
1225C22×C4—2841no—
1226C22×C4—2841no—
1227C22×C4—2841no—
1228C22×C4—2841no—
1229C22×C4—2841no—
1230C22×C4—2841no—
1231C22×C4—2841no—
1232C22×C4—2841no—
1233C22×C4—2841no—
1234C22×C4—2841no—
1235C22×C4—2841no—
1236C22×C4—2841no—
1237C22×C4—2841no—
1238C22×C4—2841no—
1239C22×C4—2841no—
1240C22×C4—2841no—
1241C22×C4—714no—
1242C22×C4—714no—
1243C22×C4—714no—
1244C22×C4—711no—
1245C22×C4—714no—
1246C22×C4—711no—
1247C22×C4—711no—
1248C22×C4—711no—
1249C22×C4—711no—
1250C22×C4—711no—
1251C22×C4—711no—
1252C22×C4—711no—
1253C22×C4—711no—
1254C22×C4—711no—
1255C22×C4—711no—
1256C22×C4—711no—
1257C22×C4—711no—
1258C22×C4—711no—
1259C22×C4—1422no—
1260C22×C4—1422no—
1261C22×C4—1422no—
1262C22×C4—1422no—
1263C22×C4—1422no—
1264C22×C4—1422no—
1265C22×C4C2×C4×D7114yes—
1266C22×C4C23×D7111yescharacteristic
1267C22×C4C23×D7111yescharacteristic
1268C22×C4C23×D7111yescharacteristic
1269C22×C4C23×D7111yescharacteristic
1270C22×C4C23×D7111yescharacteristic
1271C22×C4C23×D7111yescharacteristic
1272C22×C4C23×D7111yescharacteristic
1273C22×C4C23×D7111yescharacteristic
1274C22×C4C23×D7111yescharacteristic
1275C22×C4C23×D7111yescharacteristic
1276C22×C4C23×D7111yescharacteristic
1277C22×C4C23×D7111yescharacteristic
1278C4⋊C4—22no—
1279C4⋊C4—41no—
1280C4⋊C4—41no—
1281C4⋊C4—41no—
1282C4⋊C4—2841no—
1283C4⋊C4—2841no—
1284C4⋊C4—2841no—
1285C4⋊C4—2841no—
1286C4⋊C4—2841no—
1287C4⋊C4—2841no—
1288C4⋊C4—2841no—
1289C4⋊C4—2841no—
1290C4⋊C4—2841no—
1291C4⋊C4—2841no—
1292C4⋊C4—2841no—
1293C4⋊C4—2841no—
1294C4⋊C4—2841no—
1295C4⋊C4—2841no—
1296C4⋊C4—2841no—
1297C4⋊C4—714no—
1298C4⋊C4—714no—
1299C4⋊C4—714no—
1300C4⋊C4—714no—
1301C4⋊C4—714no—
1302C4⋊C4—714no—
1303C4⋊C4—714no—
1304C4⋊C4—1422no—
1305C4⋊C4—1422no—
1306C4⋊C4—1422no—
1307C4⋊C4—1422no—
1308C4⋊C4—1422no—
1309C4⋊C4—1422no—
1310C4⋊C4—1422no—
1311C4⋊C4C2×C4×D7114yes—
1312C22⋊C4—22no—
1313C22⋊C4—41no—
1314C22⋊C4—41no—
1315C22⋊C4—41no—
1316C22⋊C4—41no—
1317C22⋊C4—41no—
1318C22⋊C4—41no—
1319C22⋊C4—41no—
1320C22⋊C4—2841no—
1321C22⋊C4—2841no—
1322C22⋊C4—2841no—
1323C22⋊C4—2841no—
1324C22⋊C4—2841no—
1325C22⋊C4—2841no—
1326C22⋊C4—2841no—
1327C22⋊C4—2841no—
1328C22⋊C4—2841no—
1329C22⋊C4—2841no—
1330C22⋊C4—2841no—
1331C22⋊C4—2841no—
1332C22⋊C4—2841no—
1333C22⋊C4—2841no—
1334C22⋊C4—2841no—
1335C22⋊C4—2841no—
1336C22⋊C4—2841no—
1337C22⋊C4—2841no—
1338C22⋊C4—2841no—
1339C22⋊C4—714no—
1340C22⋊C4—714no—
1341C22⋊C4—714no—
1342C22⋊C4—714no—
1343C22⋊C4—714no—
1344C22⋊C4—714no—
1345C22⋊C4—714no—
1346C22⋊C4—714no—
1347C22⋊C4—1422no—
1348C22⋊C4—1422no—
1349C22⋊C4—1422no—
1350C22⋊C4C2×C4×D7114yes—
1351C22⋊C4C2×C4×D7114yes—
1352C42—22no—
1353C42—41no—
1354C42—2841no—
1355C42—2841no—
1356C42—2841no—
1357C42—2841no—
1358C42—2841no—
1359C42—2841no—
1360C42—2841no—
1361C42—2841no—
1362C42—2841no—
1363C42—714no—
1364C42—714no—
1365C42—1422no—
1366C42—1422no—
1367C42—1422no—
1368C42—1422no—
1369C42—1422no—
1370C42—1422no—
1371C42—1422no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—21no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—712no—
1391C23—712no—
1392C23—1421no—
1393C23—1421no—
1394C23—1421no—
1395C23—1421no—
1396C23—1421no—
1397C23—1421no—
1398C23—1421no—
1399C23—1421no—
1400C23—1421no—
1401C23—1421no—
1402C23—1421no—
1403C23—1421no—
1404C23C22×C4×D7112yes—
1405C23C22×C4×D7112yes—
1406C23C22×C4×D7112yes—
1407C23C24×D7111yescharacteristic
1408D4—44no—
1409D4—44no—
1410D4—44no—
1411D4—2844no—
1412D4—2844no—
1413D4—2844no—
1414D4—2844no—
1415D4—2844no—
1416D4—1428no—
1417D4—1428no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—44no—
1450C2×C4—44no—
1451C2×C4—82no—
1452C2×C4—82no—
1453C2×C4—82no—
1454C2×C4—2844no—
1455C2×C4—2844no—
1456C2×C4—2844no—
1457C2×C4—2844no—
1458C2×C4—5682no—
1459C2×C4—5682no—
1460C2×C4—5682no—
1461C2×C4—5682no—
1462C2×C4—5682no—
1463C2×C4—712no—
1464C2×C4—712no—
1465C2×C4—712no—
1466C2×C4—712no—
1467C2×C4—712no—
1468C2×C4—712no—
1469C2×C4—712no—
1470C2×C4—712no—
1471C2×C4—712no—
1472C2×C4—1421no—
1473C2×C4—1421no—
1474C2×C4—1421no—
1475C2×C4—1421no—
1476C2×C4—1421no—
1477C2×C4—1421no—
1478C2×C4—1421no—
1479C2×C4—1421no—
1480C2×C4—1421no—
1481C2×C4—1421no—
1482C2×C4—1421no—
1483C2×C4—1421no—
1484C2×C4—1421no—
1485C2×C4—1421no—
1486C2×C4—1421no—
1487C2×C4—1421no—
1488C2×C4—1421no—
1489C2×C4—1421no—
1490C2×C4—1421no—
1491C2×C4—1421no—
1492C2×C4—1421no—
1493C2×C4—1428no—
1494C2×C4—1421no—
1495C2×C4—1421no—
1496C2×C4—1421no—
1497C2×C4—1421no—
1498C2×C4—1421no—
1499C2×C4—1421no—
1500C2×C4—1421no—
1501C2×C4—1421no—
1502C2×C4—1421no—
1503C2×C4—1421no—
1504C2×C4—1421no—
1505C2×C4—1421no—
1506C2×C4C22×C4×D7112yes—
1507C2×C4C22×C4×D7112yes—
1508C2×C4C22×C4×D7112yes—
1509C2×C4C22×C4×D7112yes—
1510C2×C4#1455617312yes—
1511C22—22no—
1512C22—22no—
1513C22—22no—
1514C22—22no—
1515C22—22no—
1516C22—22no—
1517C22—22no—
1518C22—22no—
1519C22—22no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—41no—
1524C22—41no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
1530C22—41no—
1531C22—41no—
1532C22—2841no—
1533C22—2841no—
1534C22—2841no—
1535C22—2841no—
1536C22—2841no—
1537C22—2841no—
1538C22—2841no—
1539C22—2841no—
1540C22—1422no—
1541C22—1422no—
1542C22—1422no—
1543C22—1422no—
1544C22—1422no—
1545C22—1422no—
1546C22C23×C4×D7111yescharacteristic
1547C22H(5,𝔽2)×D7111yescharacteristic
1548C22H(5,𝔽2)×D7111yescharacteristic
1549C22C2×#1455617311yescharacteristic
1550C222−1+4×D7111yescharacteristic
1551C22#1798683411yescharacteristic
1552C22#1798683511yescharacteristic
1553C4—22no—
1554C4—22no—
1555C4—22no—
1556C4—22no—
1557C4—22no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—2841no—
1566C4—2841no—
1567C4—2841no—
1568C4—2841no—
1569C4—2841no—
1570C4—2841no—
1571C4—2841no—
1572C4—714no—
1573C4—1422no—
1574C4—1422no—
1575C4—1422no—
1576C4—1422no—
1577C4—1422no—
1578C4—1422no—
1579C2—42no—
1580C2—42no—
1581C2—42no—
1582C2—2842no—
1583C2—2842no—
1584C2#520×D7111yescharacteristic
1585C2#2260154411yescharacteristic
1586C2C4×#1455617311yescharacteristic
1587C2#2260265111yescharacteristic
1588C2#2260265511yescharacteristic
1589C2#2260273511yescharacteristic
1590C2#2260284411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2325C2
socle, cosocleC23×C71C25
prime radicalC2×#17986599C2
hypercenter#2325D71
hypocenterC71#34423
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2325

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22591489C2semidirect
3. #22591487C2semidirect
4. #22591484C2semidirect
5. #22591483C2semidirect
6. #22591433C2semidirect
7. #22591431C2semidirect
8. #22591403C2semidirect
9. #22591402C2semidirect
10. #22591331C2semidirect
11. #22591328C2semidirect
12. #22591326C2semidirect
13. #22591325C2semidirect
14. #22591286C2semidirect
15. #22591284C2semidirect
16. #22591247C2semidirect
17. #22591246C2semidirect
18. #22591042C2semidirect
19. #22591041C2semidirect
20. #22591037C2semidirect
21. #22591035C2semidirect
22. #22591030C2semidirect
23. #22591030C2semidirect
24. #22591030C2semidirect
25. #22591028C2semidirect
26. #22591027C2semidirect
27. #22590944C2semidirect
28. #22590850C2semidirect
29. C4×#14556100C2semidirect
30. #22590819C2semidirect
31. C71×#2325C2semidirect
32. #17986599C4semidirect
205. #14556124C2×C4semidirect
206. #14556118C2×C4semidirect
207. #14556113C2×C4semidirect
208. #14556111C2×C4semidirect
209. #14556110C2×C4semidirect
210. #14556109C2×C4semidirect
211. #14556101C2×C4semidirect
212. #14556100C2×C4semidirect
213. #14556100C2×C4semidirect
214. #14556100C2×C4semidirect
215. #14556099C2×C4semidirect
223. C4×C22⋊D71C2×C4semidirect
227. (C22⋊D71)⋊C4C2×C4semidirect
233. #14556084C2×C4semidirect
346. #121×C71C2×C4semidirect
816. #2325D71semidirect
827. C71#34423semidirect
1020. #121C4×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179865992
#225914892
#225914872
#225914842
#225914832
#225914332
#225914312
#225914032
#225914022
#225913312
#225913282
#225913262
#225913252
#225912862
#225912842
#225912472
#225912462
#225910422
#225910412
#225910372
#225910352
#225910302
#225910282
#225910272
#225909442
#225908502
C4×#145561002
#225908192
C71×#23252
#3442371